A contingency table is a tabular representation of data which falls into several categories. It shows frequencies, or less frequently, probabilities, for particular combinations of values of two qualities or discrete random variables X and Y. Each cell in the table represents a mutually exclusive combination of X-Y values. For example, consider a sample of […]

## Qualitative and Quantitative Statistics

Statistical data comes in one ogf two broad types Qualitative and Quantitative. Qualitative data is descriptive – a colour, type or one of a category. The categories that describe qualitative data may be ordered or not. We may order colours in order of their appearance in the spectrum – red/orange/yellow/green/blue/indigo/violet. If the categories are not […]

## The Venn Diagram for Three Independent Events

If three events A, B and C are mutually independent, then Suppose thatandthen The Venn diagram starts as This includes the probabilityso subtract this to obtain the diagram below. Similarly for A and C and B and c respectively. Subtractto get 0.036 Subtractto get 0.056, Finally for A, B and C respectively 0.3-(0.096+0.024+0.036)=0.144 0.4-(0.096+0.024+0.056)=0.224 0.2-(0.036+0.024+0.056)=0.084 […]

## The Standardised Score

The standardized score is a statistical tool that allows comparison of related quantities that are normally distributed. A very good use is test scores. When a student wishes to compare their own results with everybody elses, they may stanaridize their scores to find the percentile in which they lie. Suppose one student recorded his marks […]

## Residuals

Suppose we have a set of data pointsrelating one quantity to another. We can plot the points on a scattergraph and find the equation of the regression line ofonso thatis expressed linearly in terms ofIf we take one of the points from which the equation of the regression line was calculated,he regression line predicts, for […]

## Pascal’s Triangle

Pascal’s triangle provides a quick and easy way to calculate the coefficients of the binomial expansion, The entries in the table are calculated by adding the entties in each table immediately above to the left and right, with the exceptions of the first and last entires in each row, which are both 1 as show […]

## Outliers

An outlier of a statistical sample is an extreme value – the very rich man, the dwarf, the Spruce Goose – a large plane built by reclusive billionaire Howard Hughes. It flew only once and now sits in a museum – a monument to people with too much money. There are many methods of classifying […]

## Advanced Questions on Venn Diagrams

More complicated question on Venn diagrams involve the use of simultaneous equations, or the introduction of a dummy variable x. ExampleSketch the Venn diagram. (1) (2) Divide (1) by (2) to get Substitute these into the equation Thenand from (1) We can draw the Venn diagram. Example:andare independent.andFind the possible values of and draw a […]

## Permutations

Permutations is that part of statistics involving arrangements of objects, some of which fall in the same group and some of which fall in different groups. Each object is distinct from all the other objects, so we can tell each one apart, and if two objects are interchanged, this is a different arrangement of the […]

## Combinations – When Order of Precedence is Not Taken into Account

We have to pick from a selection of objects, and need to know, in how many ways canobjects be picked from a choice of There are complications. If the is no order of preference, then the order of the selection does not matter. If you are choosing which library books to take out, then the […]